Problem: Find $\lim_{x\to 1}\dfrac{x-11}{x+7}$. Choose 1 answer: Choose 1 answer: (Choice A) A $-2$ (Choice B) B $-\dfrac{5}{4}$ (Choice C) C $\dfrac{3}{2}$ (Choice D) D The limit doesn't exist
Solution: Let's try to find the limit using direct substitution. $\begin{aligned} \lim_{x\to 1}\dfrac{x-11}{x+7}&=\dfrac{1-11}{1+7} \\\\ &=\dfrac{-10}{8} \\\\ &=-\dfrac{5}{4} \end{aligned}$ We got a finite number. Since $\dfrac{x-11}{x+7}$ is continuous across its domain, we can determine that $\lim_{x\to 1}\dfrac{x-11}{x+7}$ is indeed equal to $-\dfrac{5}{4}$. In conclusion, $\lim_{x\to 1}\dfrac{x-11}{x+7}=-\dfrac{5}{4}$.